In summary, for those who do not follow such things (and I have noticed that "graphene" is among the top keywords bringing people to this site, so it is quite possible you do follow such things): Graphene was "discovered," or if you will isolated, by Geim and Novoselov in 2004, by peeling off layers of graphite with scotch tape. It is essentially an indefinitely large aromatic molecule, and the flat, two-dimensional form of the buckyball or the buckytube. For a variety of reasons I won't get into here, it has numerous potential applications in electronics and nanotechnology, and is quite interesting all around.

It had never actually occurred to me prior to 2004 that graphene needed to be "discovered." I had always been taught that graphite, as a major allotrope of carbon, consisted of one-atom-thick sheets of carbon atoms arranged in a hexagonal lattice, and that this had been known for quite a while (since at least the advent of X-ray crystallography). Thus it really shouldn't have been too much of a conceptual leap to assume that, in fact, such sheets existed (though apparently the prevailing view was that the sheets would "roll up" when isolated). I still have a hard time wrapping my mind around the fact that it took until 2004 to actually discover this. Particularly with all the research that's gone on with fullerenes since the '80s, you'd think somebody, somewhere, would've taken the time to actually isolate a sheet of graphite. Apparently it is somewhat difficult, but crap I have scotch tape and pencils lying around, by all rights that Nobel could've been mine.

I have been reading about the PAH world hypothesis, and have come to see it as an intriguing indicator of the potentially hexagonal origins of life on earth.

Essentially, it is conjectured that, since polycyclic aromatic hydrocarbons are among the most common spaceborne molecules in the known universe, they would have likely been a constituent in the primordial seas of Earth, where they could have provided some sort of scaffolding or template on which early biological polymers such as RNA could assemble, thus solving a frequently-raised objection to the RNA world hypothesis that RNA is too fragile and transient to survive long outside of an extant cell or similar protective environment. By providing a structural backbone on which reasonably complex RNA strands and such could self-assemble, the PAH world would have given early pre-cellular life a fighting chance of finding its way into protective lipid bubbles, weird mineral formations, or what have you, where given enough replicative iterations it presumably developed into proper cellular life as we know it.

Carbon nanotubes are allotropes of carbon in the fullerene family, discovered in 1991 (more or less). Rolling sheets of graphene at different chiral angles creates fullerenes with different electrical properties, making them highly suitable for use in nanoscale electronics, as well as other nanotechnological applications. Nanotubes can be either single-walled or multi-walled, and can be joined together with other fullerenes to form a wide variety of structures. Due to their high tensile strength, diverse electrical and mechanical properties, and versatile carbon chemistry, nanotubes—along with graphene and other fullerenes—represent an important hexagonal contribution to the emerging field of nanotechnology.

"Graphene is a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities. It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite."